Applied Mathematics and Communications Institute Performance Analysis of Mixture of Unicast and Multicast Sessions in 5G NR Systems Andrey Samuylov, Dmitri Moltchanov, Alesia Krupko, Roman Kovalchukov, Faina Moskaleva, and Yuliya Gaidamaka Applied Mathematics and Communications Institute

Outline Features of mmWave in 3GPP New Radio (NR) air interface System model for 3GPP NR multicasting Mathematical model as a queuing system with combination of unicast and multicast traffic Numerical analysis

SYSTEM MODEL FOR 3GPP NR MULTICASTING Network Deployment (1/2) System: NR access point (AP) with unicast and multicast sessions Features: propagation specifics of mmWave band linear antenna arrays at both AP and UE random resource requirements induced by locations of UEs human blockage phenomenon Fig. 1. Coexistence of sessions at a single NR AP

SYSTEM MODEL FOR 3GPP NR MULTICASTING Network Deployment (2/2) Metrics: unicast session drop probability multicast session drop probability system resource utilization Goal: determine optimal AP intersite distance for 3GPP NR systems Fig. 1. Coexistence of sessions at a single NR AP

Outline Features of mmWave in 3GPP New Radio (NR) air interface System model for 3GPP NR multicasting Assumptions Multicast sessions: “transparent” service CDFs for unicast and multicast random resources requirements Propagation, Blockage and Antenna Models Mathematical model as a queuing system with combination of unicast and multicast traffic Numerical analysis

SYSTEM MODEL FOR 3GPP NR MULTICASTING Assumptions Single AP: rA - radius of the coverage area of NR AP Coexistence of unicast and multicast traffic: BM - amount of resources for a multicast session, random variable (RV) BU - amount of resources for a unicast session, RV Unicast session: “traditional” service - the amount BU of resources should be allocated for each new session Multicast session: “transparent” service

SYSTEM MODEL FOR 3GPP NR MLTICASTING Multicast sessions: “transparent” service

SYSTEM MODEL FOR 3GPP NR MULTICASTING CDFs for random resources requirements Unicast session: Suppose RV BU=const=d. Multicast session: 𝑏1<𝑏2<…𝑏𝐾 – the values of RV BM with CDF Pr⁡{ 𝐵 𝑀 =𝑏𝑘}=ф𝑘, 𝑘=1,…,𝐾, ф𝑘 - the probability that multicast session requires 𝑏𝑘 resources, 𝑘=1,…,𝐾

SYSTEM MODEL FOR 3GPP NR MULTICASTING Propagation, Blockage and Antenna Models hA – height of AP hU – height of UEs hB – height of cylindrical blocker rB – radius of cylindrical blocker λB – intensity of spatial Poisson process Fig. 2. LoS blockage zone

Outline Features of mmWave in 3GPP New Radio (NR) air interface System model for 3GPP NR multicasting Mathematical model as a queuing system with combination of unicast and multicast traffic Queuing model AP Characterizations AP Resource Request Distribution Numerical analysis

SYSTEM MODEL FOR 3GPP NR MULTICASTING Queuing model: parameters Fig. 3. Queuing system with combination of unicast and multicast traffic.

SYSTEM MODEL FOR 3GPP NR MULTICASTING Queuing model: Markov chain (1/2) 𝐶 - amount of resources in the system 𝑑 - resources demand for unicast sessions 𝑏1<𝑏2<…𝑏𝐾 – resources demands for multicast sessions 𝑛(𝑡) – number of unicast sessions in the system at time t 𝑟(𝑡) – total amount of resources occupied in the system at time t 𝑟(𝑡)= 𝑈 𝑈 (𝑡)+ 𝑈 𝑀 (𝑡) (𝑛(𝑡), 𝑟(𝑡)) - state of the system at time t (2) Mathematical model: 𝑛 𝑡 ,𝑟 𝑡 , 𝑡>0 – Markov chain 𝑋= 𝑛,𝑟 :0≤𝑛≤ 𝐶 𝑑 ,0≤𝑟≤𝐶 - set of states

SYSTEM MODEL FOR 3GPP NR MULTICASTING Queuing model: Markov chain (2/2) Fig. 4. Markov chain state transition diagram.

Queuing model: performance metrics Mean amount of occupied resources in the system: (7) Set of unicast session drop states: (8) Unicast session drop probability: (9) Set of multicast session drop states: (10) (11) Multicast session drop probability:

AP Coverage Characterizations Smin - minimum SNR a system may tolerate γ - path loss exponent hA and hU - heights of AP and UE PT - AP transmit power GT and GR - AP transmit and UE receive antenna gains, respectively N0 - thermal noise at receiver LB=15 dB - blockage-induced losses, A - constant in the path loss model 𝐴 𝑟 −𝛾 To find AP coverage: 𝑆 𝑚𝑖𝑛 = 𝐶 𝐵 ( 𝑟 𝐴 + [ ℎ 𝐴 − ℎ 𝑈 ] 2 ) −𝛾/2 , Solving (12) we arrive to 𝑟 𝐴 = ( 𝐶 𝐵 / 𝑆 𝑚𝑖𝑛 ) 𝛾/2 + ( ℎ 𝐴 − ℎ 𝑈 ) 2 (12) (13)

AP Resource Request Characterizations CDF of the distance between UE and AP 𝐹 𝐷 𝑦 = 𝑦 2 − ℎ 𝐴 − ℎ 𝑈 2 𝑟 𝐴 2 , The distribution of SNR SnB in non-Blocking conditions: 𝐹 𝑆 𝑛𝐵 𝑦 =1− 𝐹 𝐷 ( 𝛾 𝐶 𝑛𝐵 /𝑦 ), The distribution of SNR SB in Blocking conditions: 𝐹 𝑆 𝐵 𝑦 =1− 𝐹 𝐷 ( 𝛾 𝐶 𝐵 /𝑦 ), Blockage probability at the distance x [10]: 𝑝 𝐵 𝑥 =1− 𝑒 −2 𝜆 𝐵 𝑟 𝐵 𝑥 ℎ 𝐵 − ℎ 𝑈 ℎ 𝐴 − ℎ 𝑈 + 𝑟 𝐵 . (14) (15) (16) (17)

фk = 𝑃𝑟 𝑠 𝑘 ≤𝑆< 𝑠 𝑘+1 =𝐹 𝑆 𝑠 𝑘+1 − 𝐹 𝑆 𝑠 𝑘 . AP Resource Request Distribution With obtained CDFs 𝐹 𝑆 𝑛𝐵 𝑦 , 𝐹 𝑆 𝐵 𝑦 , 𝑝 𝐵 𝑥 we get CDF for SNR 𝑆 𝐹 𝑆 𝑦 = 1− 𝑝 𝐵 𝐹 𝑆 𝑛𝐵 𝑦 + 𝑝 𝐵 𝐹 𝑆 𝐵 𝑦 , where 𝑝 𝐵 = 0 𝑟 𝐴 𝑝 𝐵 𝑥 𝑑𝑥 . (18) With given SNR margins 𝑠1<𝑠2<…<𝑠𝐾 for 𝐾 different MCS schemes we obtain resource request distribution фk = 𝑃𝑟 𝑠 𝑘 ≤𝑆< 𝑠 𝑘+1 =𝐹 𝑆 𝑠 𝑘+1 − 𝐹 𝑆 𝑠 𝑘 . (19)

Outline Features of mmWave in 3GPP New Radio (NR) air interface System model for 3GPP NR multicasting Mathematical model as a queuing system with combination of unicast and multicast traffic Numerical analysis

Drop probabilities vs sessions arrival intensities

Drop probabilities vs sessions service intensities

System resource utilization vs sessions arrival intensities

Conclusions The model of the service process at NR AP is served a mixture of unicast and multicast traffic that takes into account propagation specifics of a mmWave band, linear antenna arrays at both AP and UEs stochastic locations of users The increase in multicast session arrival rate and/or mean service time results in a decrease of the multicast session drop probability. The proposed model can be used for dimensioning of prospective NR systems.

Thank you! Faina Moskaleva Tel.: +7 916 955 72 00 Email: moskaleva_fa@rudn.ru